A pilot signal (or preamble) is commonly used for communication systems to enable the receiver to perform a number of critical functions, including but not limited to, the acquisition and tracking of timing and frequency synchronization, the estimation and tracking of desired channels for subsequent demodulation and decoding of the information data, the estimation and monitoring of the characteristics of other channels for handoff, interference suppression, etc. Several pilot schemes can be utilized by communication systems, and typically comprise the transmission of a known sequence at known time intervals. A receiver, knowing the sequence and time interval in advance, utilizes this information to perform the above-mentioned functions.
Several criteria are important when determining pilot sequences for communication systems. Among these criteria is the ability to have good auto-correlation for each of the pilot sequences utilized, and at the same time the ability to have good cross-correlation between any two different pilot sequences. Auto- and cross-correlation are sequences themselves corresponding to different shifts. Auto-correlation at shift-d is defined as the result of summing over all entries after an element-wise multiplication between the sequence and its conjugated replica after shifting it by d entries (d can be positive or negative for right or left shift). Cross-correlation at shift-d is defined as the result of summing over all entries after an element-wise multiplication between a sequence and another sequence that is conjugated and shifted by d entries with respect to the first sequence. “Good” auto-correlation results in each pilot sequence having a minimal auto-correlation value at all shifts of interest (i.e., a range of d, except for d=0). “Good” cross-correlation results in the pilot sequence having a minimal cross-correlation value at all shifts of interest. When the auto-correlation is zero at all d, except for d=0, it is referred to as “ideal” auto-correlation. Since the cross-correlation of two sequences that have ideal auto-correlation cannot be zero at all d, the minimum of the maximum cross-correlation values at all shifts can be reached only when the cross-correlation at all d is equal in amplitude, which is referred to as having “optimal” cross-correlation.
Since the received signal after propagation consists of replicas of the delayed pilot sequence after some scaling factors, the ideal auto-correlation property of the pilot makes the estimation of the channel scaling factors at different delays possible. The optimal cross-correlation property between any two pilot sequences will minimize the interference effect seen at the receiver that is caused by any pilot sequences other than the desired one (i.e., one that the receiver is tuned to). Good cross-correlation makes the detection of the desired pilot signal and the estimation of the desired channel characteristics more reliable, which enables the receiver to perform synchronization and channel estimation more reliably.
Various techniques have been used in the past to design systems with efficient pilot sequences. For example, in the current CDMA-based cellular system, the pilot sequence in a cell is a Walsh code that is scrambled by a cell-specific scrambling code (long code). This effectively randomizes the pilot sequence for each cell. Channel estimation of the neighboring base stations, when required during a soft handoff, is simply performed by correlating the received signal with the neighboring base station's long code scrambled pilot sequences. But the cross-correlation property of two random pilot sequences is not optimal, and thus a larger channel estimation error can be expected. Therefore, a need exists for a method and apparatus for pilot signal or preamble transmission that optimizes both the cross correlation between pilot signals, as well as optimizing each pilot signal's auto correlation.